Untitled

import numpy as np
import matplotlib.pyplot as plt

n = 101
P = np.array([[0, 0.2, 0.5, 0.3],
              [0.5, 0, 0.5, 0],
              [0.3, 0.7, 0, 0],
              [0.1, 0, 0, 0.9]])
x = np.array(np.ones(n, dtype=int))
x[0] = 0

for t in range(0, n - 1):
    x[t + 1] = np.min(np.where(np.cumsum(P[x[t], :]) > np.random.rand()))

x = x + 1  # add 1 to all elements of the vector x

plt.plot(np.array(range(0, n)), x, 'o')
plt.plot(np.array(range(0, n)), x, '--')
plt.show()